Why should Shmuel cease mourning?
Malbim: Prolonged mourning can be due to (a) the great level of the one who was lost. I despised him from being king! (b) [It can be if] there is no replacement for him. Here, you will anoint a new king!
Is a full horn of oil needed to anoint?
Radak (from Kerisus 5b): Yes. He anoints in the shape of a crown between Risei Einav. 1 The rest he pours on the head.
Normally these are the eyelashes, but here, surely it means like the Bartenura explains (Kerisus 1:1), between the eyebrows. (PF)
Why did He say "Karnecha"?
Radak: This horn was designated to anoint kings of Beis David 1 . Nevi'im designated it. It was in the Ohel Mo'ed, with the Kli of Shemen ha'Mishchah. It is incumbent on Nevi'im to anoint kings. Even though Tzadok ha'Kohen anointed Shlomo, Nasan ha'Navi was there with him.
Malbim: It is special for you to anoint kings. Sha'ul was anointed from a flask. His kingship did not last, for the nation chose to have a king. Hashem chose a tall man, who would find grace in the eyes of the nation. Now is the time for a king who will sit on Hashem's throne and be pleasing to Hashem, and not only to the nation. Chanah hinted to this (2:1) "Ramah Karni" - my horn is raised, but not my flask (Megilah 14a.. David and Shlomo were anointed with a horn (of oil), and their kingships lasted. Sha'ul and Yehu were anointed with flasks, and their kingships did not last.)
Now, it was not yet known that David will be king. 'Beis David' refers to the permanent kingship that Hashem will choose. However, this implies that when Sha'ul was anointed from a flask, it was known that his kingship will not be permanent. "Hechin
What is "Beis ha'Lachmi"?
Rashi: It is in Beis Lechem. The same applies whenever a name has two words, like Beis Lechem, Beis Shemesh, Beis Kel, Kiryas Arba. If one comes to add a Hei, he puts it in the middle, e.g. Kiryas ha'Arba Beis ha'Keli, Beis ha'Lachmi.
Why did He say "Li Melech"?
Radak: He will be for My service and heed Me for everything I command, unlike Sha'ul, who transgressed My word.
